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Applied Physics 186 Investigative Project

Presented by: Elexis Mae A. Torres

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M. Turk and A. Pentland, "Eigenfaces for Recognition", Journal of Cognitive Neuroscience, vol. 3,

no. 1, pp. 71-86, 1991, hard copy 3

Face Recognition

To establish a computational model that could detect anddistinguish human faces from each other.

Applications:

o criminal identification

o security systemso image and film processing

o human-computer interaction

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Sheng Zhang and Matthew Turk (2008) Eigenfaces. Scholarpedia, 3(9):4244. 4

Face Recognition via PCA

o Sirovich and Kirby 1987

used principal components to represent human faces.

o Turk and Pentland 1991

extended to face detection and recognition.

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1Jolliffe, I. (1986). Principal Component Analysis. Springer Verlag. 5

Principal Components Analysis

to reduce the dimensionality of a data set consisting of a large number of

interrelated variables, while retaining as much as possible of the variation present in the

data set. This is achieved by transforming to a new set of variables, the principal

components (PCs), which are uncorrelated, and which are ordered so that the first few

retain most of the variation present in all of the original variables. 1

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7/251Jolliffe, I. (1986). Principal Component Analysis. Springer Verlag. 7

3 Main Steps

1. Obtaining a training set

2. Derivation of eigenfaces via PCA

3. Face recognition using a test set

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Training Set

o consists of five 64x64 grayscaled face images

o used detectfaces(), imcrop(), imresize()

o histogram manipulation

o transformed into a 4096x5 matrix matrix T

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Derivation of Eigenfaces

1. calculated for the mean face

rowmean

2. subtracted mean face from training set

A = T - rowmean

3. derived covariance matrix

C = ATA4. applied pca() on C

5. multiplied eigenvectors toA to get eigenfaces

[ef1,ef2,ef3, ef4]

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Recognizing Face Images in Test Set

1. subtracted mean face from input image

diffim = inputimrowmean

2. calculate for the coefficients/weights of each eigenface

w1 = ef1*diffim

3. sum up to reconstruct input image

reim = w1*(u1(i)) + w2*(u2(i)) + w3*(u3(i)) + w4*(u4(i)

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Training Set

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Training Set and Mean Face

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Difference MatrixA

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Four Eigenfaces

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Four Eigenfaces

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Results and DiscussionTest Set 1

Face images of people from the training set

Inputim :

Reim :

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Inputim :

Reim :

Results and DiscussionTest Set 1

Face images of people from the training set

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Results and DiscussionTest Set 1

Face images of people from the training set

Inputim :

Reim :

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Face images of people NOT in the training set

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Inputim :

Reim :

Results and DiscussionTest Set 2

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Non-faces

Results and DiscussionTest Set 3

Inputim :

Reim :

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Comparing reconstructed images

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Faces :

Non-faces :

Results and DiscussionTesting Set 3

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SUCCESS

faces already in the training set

facial expressions

face orientation

FAILURE

faces not in the training set

non-faces

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